The minimum volume of urine required by the kidneys to excrete the waste products of metabolism is about half a liter per day. Since we lose another half liter via sweat, breathing, and feces, the net intake required to maintain water balance is about one liter per day under normal conditions. Drinking more than this simply results in more dilute urine--the same absolute amount of "toxins" will still be excreted. There is no rationale behind the common injunction that the "2 liters or more a day" should be pure water alone.
However, water is extremely serious as far as your liver and your basic well-being go. You can live 40 days without food but only about 3 days without water, and, depending on your diet, you’ll probably feel rather unwell long before you die. The basic truth is that you do not need to “wash” your blood, and extra water does not help cleanse your body’s tissues, nor does it, of itself, stimulate the action of your lymphatic system. The liver removes waste and toxins from the blood and it is excreted or stored safely in fatty tissues until it can be excreted.
The lymphatic system is stimulated by exercise, and you don’t have to work out to get enough for healthy lymphatic function. The kidneys are not primarily organs of excretion as such. The kidney's primary function is to maintain the balance of the blood. To do so they remove excesses of substances that the body cannot use at the time, other non-toxic blood byproducts, and some drug residues. Urine is not “waste” in same the way fasces are. Unless you have urinary infection urine is sterile, and, in actual fact, drinkable if not exactly palatable.
The fact is that the water in your body is constantly circulating and constantly being filtered. It does not need to be changed but it does need to be topped up to account for losses through urination, respiration, perspiration, and excretion. Another important factor is maintaining the proper alkaline balance in the tissues. Without that the body needs more water to dilute the imbalance and the body’s cleansing systems will be less effective.
Our metabolism produces plenty of toxins, which the kidney does a good job of excreting. It is true that the symptoms caused by kidney failure can be helped by changes in diet, but this is a fairly extreme situation. Drinking more water than the minimum needed would not make any significant difference to the elimination of waste products for the vast majority of us who have normal renal function.
After all the most important thing to consider about water and detoxification is that once a water molecule has been absorbed across the gut, how can the body tell whether it originated from pure water or a more interesting flavored beverage? There are minor diuretic effects from alcohol and components of tea and coffee, but provided we drink when we feel thirsty, these are easily compensated for. Simply drinking enough water when you feel thirsty, along with a steady diet and exercise should in most cases keep your body cleansed.